Did Hubble can it wrong?

[Surgenator]

You're using this formula wrongly. In that link, they are talking about a light emanating from inside a star with a radius less than a Schwarzchild radius, which is the radius of a black hole. The point the author is making is in that case, light won't be able to escape. My thought experiment is not about light emanating from the inside of the earth, but from an emitter standing at a distance d above the ground. Different experiments require that you use the math properly.

I am using the equation correctly.

and R^* the distance between the center of mass of the gravitating body and the point at which the photon is emitted. The redshift is not defined for photons emitted inside the Schwarzschild radius, the distance from the body where the escape velocity is greater than the speed of light. Therefore this formula only applies when R^* is at least as large as r_s.

Sorry but if you can't do the math, you're not in a position to criticize.

Oh, I can do the math. I don't want to waste my time doing so when I can't point out that your claim is wrong through a thought experiments.

My two arguments address your claim that "Doppler Effect = Gravitational Shift" through thought experiments. The first one takes the case of the same gravitational potential but at different distances away.

That's why I put 3 different emitters at 3 different distances. But I show that for all these cases, you get one general equation.

The wavelength shift of your 3 emitters would be the same when they're light years away.

The second is different gravitational potentials but at the same distance away.

That is not possible for a gravitational potential. It's inversely proportional with distance. So at equal distance, the gravitational potential has to be the same.

Your forgetting about the mass of the object. Gravitational potential = GM/r.